Change the scale of the viewport
You can change the scale of the whole scene to metric .001 (one thousandth of a meter=1mm).

Version 2.8X


Version 2.7X


But to be able to work at such small scale you also have to adjust the scale on the viewport as well:

For 2.8X The settings are in the overlay section.


For 2.7X they are in the Numeric Panel (N)


Here's what a 1mm x 1mm x 1mm object looks like in with such scaling: